I’ve just noticed that Air Berlin codeshares on the Etihad flights out of Melbourne to Abu Dhabi with onward connections to Europe. I’ve been trying to decide if this meets Qantas FF’s definition of an ‘eligible flight’ for the purposes of earning status credits and points.

Isn’t too difficult to discover. You just have to look at status credit earn for airberlin on Qantas website, which says “Qantas Points and Status Credits are earned on all eligible fare or booking classes, except on airberlin and airberlin affiliate codeshare flights operated by an airline other than Qantas or a oneworld® alliance airline.” Etihad is an example of an airberlin codeshare flight operated on an airline other than oneworld, so no, you cannot earn Qantas status credits.